In a world where Bush dies on 9/11, who is the Republican nominee in 2004?

Simple enough question: in a world where Bush dies on 9/11 (or by choking a pretzel a few months later), who would be in the strongest position to win the Republican presidential nomination in 2004? The incumbent, Dick Cheney, seems like someone who would not want mount his own bid for the presidency. Of course, he and the other major players in the Bush Administration, such as Donald Rumsfeld and Paul Wolfowitz, would want someone who would essentially stay the course with their policies, especially with respect to foreign policy, and could conceivably fast-track a successor by appointing them as Vice President.

So... who are the likely options? John McCain was the runner up in 2000, would go on to win the GOP nomination in 2008 in our timeline, and was a notable hawk, which would be important with the War on Terror in full swing. However, I get the sense that there was bad blood between him and the Bush camp, so Cheney and company may be reticent to throw their weight behind him, at least to begin with. Rudy Giuliani had a strong profile as “America’s Mayor” for his handling of 9/11 in New York City, but as we saw in our timeline’s 2008 election, he was just not a great candidate, and his positions on social issues such as abortion make him a bad fit for the Republican base regardless. Would the difference of four years have been significant in this situation? Might the Republican establishment have successfully thrown their weight behind a relatively generic politician such as George Allen, Bill Frist or Fred Thompson?
 
Jeb could be well positioned to take the nomination and win the election to, if he wants it and if Cheney doesn't stop him.
 

SsgtC

Banned
It's probably Cheney. In OTL he didn't really want to be President, but here, if he's been in office for four years already, he would likely accept that should run for reelection. The only way I don't see him running is if it's very plainly obvious that he'll lose. In that case, I could see him declining to run "for reasons of ill health." In that case, it's probably McCain's nomination to lose.
 
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